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Kcv channels from plant viruses represent the autonomous pore module of potassium channels, devoid of any regulatory domains. These small proteins show very reproducible single-channel behavior in planar lipid bilayers. Thus, they are an optimum system for the study of the biophysics of ion transport and gating. Structural models based on homology modeling have been used successfully, but experimental structural data are currently not available. Here we determine the size of the cytosolic pore entrance by studying the blocker kinetics. Blocker binding and dissociation rate constants ranging from 0.01 to 1000 ms -1 were determined for different quaternary ammonium ions. We found that the cytosolic pore entrance of Kcv NTS must be at least 11 Å wide. The results further indicate that the residues controlling a cytosolic gate in one of the Kcv isoforms influence blocker binding/dissociation as well as a second gate even when the cytosolic gate is in the open state. The voltage dependence of the rate constant of blocker release is used to test, which blockers bind to the same binding site.

Most potassium channels have two main gate locations, hosting an inner gate at the cytosolic entrance and a filter gate in the selectivity filter; the function of these gates is in many channels coupled. To obtain exclusive insights into the molecular mechanisms that determine opening and closing of the filter gate, we use a combination of single-channel recordings and gating analysis in the minimal viral channel Kcv NTS . This channel has no inner gate, and its fast closing at negative voltages can therefore be entirely assigned to the filter gate. We find that mutations of S42 in the pore helix severely slow down closing of this filter gate, an effect which is not correlated with hydrogen bond formation by the amino acid at this position. Hence, different from KcsA, which contains the critical E71 in the equivalent position forming a salt bridge, the coupling between selectivity filter and surrounding structures for filter gating must in Kcv NTS rely on different modes of interaction. Quantitative analysis of concatemers carrying different numbers of S42T mutations reveals that each subunit contributes the same amount of ∼ 0.4 kcal/mol to the energy barrier for filter closure indicating a concerted action of the subunits. Since the mutations have neither an influence on the unitary current nor on the voltage dependency of the gate, the data stress that the high subunit cooperativity is mediated through conformational changes rather than through changes in the ion occupation in the selectivity filter., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Modulating the activity of ion channels by blockers yields information on both the mode of drug action and on the biophysics of ion transport. Here we investigate the interplay between ions in the selectivity filter (SF) of K + channels and the release kinetics of the blocker tetrapropylammonium in the model channel Kcv NTS . A quantitative expression calculates blocker release rate constants directly from voltage-dependent ion occupation probabilities in the SF. The latter are obtained by a kinetic model of single-channel currents recorded in the absence of the blocker. The resulting model contains only two adjustable parameters of ion-blocker interaction and holds for both symmetric and asymmetric ionic conditions. This data-derived model is corroborated by 3D reference interaction site model (3D RISM) calculations on several model systems, which show that the K + occupation probability is unaffected by the blocker, a direct consequence of the strength of the ion-carbonyl attraction in the SF, independent of the specific protein background. Hence, Kcv NTS channel blocker release kinetics can be reduced to a small number of system-specific parameters. The pore-independent asymmetric interplay between K + and blocker ions potentially allows for generalizing these results to similar potassium channels., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Gabriel, Hansen, Urban, Drexler, Winterstein, Rauh, Thiel, Kast and Schroeder.)

It has become increasingly apparent that the lipid composition of cell membranes affects the function of transmembrane proteins such as ion channels. Here, we leverage the structural and functional diversity of small viral K+ channels to systematically examine the impact of bilayer composition on the pore module of single K+ channels. In vitro-synthesized channels were reconstituted into phosphatidylcholine bilayers ± cholesterol or anionic phospholipids (aPLs). Single-channel recordings revealed that a saturating concentration of 30% cholesterol had only minor and protein-specific effects on unitary conductance and gating. This indicates that channels have effective strategies for avoiding structural impacts of hydrophobic mismatches between proteins and the surrounding bilayer. In all seven channels tested, aPLs augmented the unitary conductance, suggesting that this is a general effect of negatively charged phospholipids on channel function. For one channel, we determined an effective half-maximal concentration of 15% phosphatidylserine, a value within the physiological range of aPL concentrations. The different sensitivity of two channel proteins to aPLs could be explained by the presence/absence of cationic amino acids at the interface between the lipid headgroups and the transmembrane domains. aPLs also affected gating in some channels, indicating that conductance and gating are uncoupled phenomena and that the impact of aPLs on gating is protein specific. In two channels, the latter can be explained by the altered orientation of the pore-lining transmembrane helix that prevents flipping of a phenylalanine side chain into the ion permeation pathway for long channel closings. Experiments with asymmetrical bilayers showed that this effect is leaflet specific and most effective in the inner leaflet, in which aPLs are normally present in plasma membranes. The data underscore a general positive effect of aPLs on the conductance of K+ channels and a potential interaction of their negative headgroup with cationic amino acids in their vicinity., (© 2021 Winterstein et al.)

Many potassium channels show voltage-dependent gating without a dedicated voltage sensor domain. This is not fully understood yet, but often explained by voltage-induced changes of ion occupation in the five distinct K + binding sites in the selectivity filter. To better understand this mechanism of filter gating we measured the single-channel current and the rate constant of sub-millisecond channel closure of the viral K + channel Kcv NTS for a wide range of voltages and symmetric and asymmetric K + concentrations in planar lipid membranes. A model-based analysis employed a global fit of all experimental data, i.e., using a common set of parameters for current and channel closure under all conditions. Three different established models of ion permeation and various relationships between ion occupation and gating were tested. Only one of the models described the data adequately. It revealed that the most extracellular binding site (S0) in the selectivity filter functions as the voltage sensor for the rate constant of channel closure. The ion occupation outside of S0 modulates its dependence on K + concentration. The analysis uncovers an important role of changes in protein flexibility in mediating the effect from the sensor to the gate.

Lipid bilayers provide many benefits for ion channel recordings, such as control of membrane composition and transport molecules. However, they suffer from high membrane capacitance limiting the bandwidth and impeding analysis of fast gating. This can be overcome by fitting the deviations of the open-channel noise from the baseline noise by extended beta distributions. We demonstrate this analysis step-by-step by applying it to the example of viral K +  channels (Kcv), from the choice of the gating model through the fitting process, validation of the results, and what kinds of results can be obtained. These voltage sensor-less channels show profoundly voltage-dependent gating with dwell times in the closed state of about 50 μs. Mutations assign it to the selectivity filter., (© 2017 The Authors. FEBS Letters published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies.)

The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

Transport activity through the mutant D44A of the M2 proton channel from influenza virus A was measured in excised inside-out macro-patches of Xenopus laevis oocytes at cytosolic pH values of 5.5, 7.5 and 8.2. The current-voltage relationships reveal some peculiarities: 1. "Transinhibition", i.e., instead of an increase of unidirectional outward current with increasing cytosolic H(+) concentration, a decrease of unidirectional inward current was found. 2. Strong inward rectification. 3. Exponential rise of current with negative potentials. In order to interpret these findings in molecular terms, different kinetic models have been tested. The transinhibition basically results from a strong binding of H(+) to a site in the pore, presumably His37. This assumption alone already provides inward rectification and exponential rise of the IV curves. However, it results in poor global fits of the IV curves, i.e., good fits were only obtained for cytosolic pH of 8.2, but not for 7.5. Assuming an additional transport step as e.g. caused by a constriction zone at Val27 resulted in a negligible improvement. In contrast, good global fits for cytosolic pH of 7.5 and 8.2 were immediately obtained with a cyclic model. A "recycling step" implies that the protein undergoes conformational changes (assigned to Trp41 and Val27) during transport which have to be reset before the next proton can be transported. The global fit failed at the low currents at pHcyt = 5.5, as expected from the interference of putative transport of other ions besides H(+). Alternatively, a regulatory effect of acidic cytosolic pH may be assumed which strongly modifies the rate constants of the transport cycle.

The current of the minimal viral K(+) channel Kcv(PCBV-1) heterologously expressed in Xenopus oocytes is strongly inhibited by reactive oxygen species (ROS) like H(2)O(2). Possible targets for the ROS effect are two cysteines (C53 and C79) and four methionines (M1, M15, M23, and M26). The C53A/C79A and M23L/M26L double mutations maintained the same ROS sensitivity as the wild type. However, M15L as a single mutant or in combination with C53A/C79A and/or M23L/M26L caused a complete loss of sensitivity to H(2)O(2). These results indicate a prominent role of M15 at the cytosolic end of the outer transmembrane helix for gating of Kcv(PCBV-1). Furthermore, even though the channel lacks a canonical voltage sensor, it exhibits a weak voltage sensitivity, resulting in a slight activation in the millisecond range after a voltage step to negative potentials. The M15L mutation inverts this kinetics into an inactivation, underlining the critical role of this residue for gating. The negative slope of the I-V curves of M15L is the same as in the wild type, indicating that the selectivity filter is not involved.

Single-channel current-voltage (IV) curves of human large-conductance, voltage- and Ca(2+)-activated K(+) (BK) channels are quite linear in 150 mM KCl. In the presence of Ca(2+) and/or Mg(2+), they show a negative slope conductance at high positive potentials. This is generally explained by a Ca(2+)/Mg(2+) block as by Geng et al. (2013. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.201210955) in this issue. Here, we basically support this finding but add a refinement: the analysis of the open-channel noise by means of β distributions reveals what would be found if measurements were done with an amplifier of sufficient temporal resolution (10 MHz), namely that the block by 2.5 mM Ca(2+) and 2.5 mM Mg(2+) per se would only cause a saturating curve up to +160 mV. Further bending down requires the involvement of a second process related to flickering in the microsecond range. This flickering is hardly affected by the presence or absence of Ca(2+)/Mg(2+). In contrast to the experiments reported here, previous experiments in BK channels (Schroeder and Hansen. 2007. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.200709802) showed saturating IV curves already in the absence of Ca(2+)/Mg(2+). The reason for this discrepancy could not be identified so far. However, the flickering component was very similar in the old and new experiments, regardless of the occurrence of noncanonical IV curves.

One major determinant of the efficacy of antibiotics on gram-negative bacteria is the passage through the outer membrane. During transport of the fluoroquinolone enrofloxacin through the trimeric outer membrane protein OmpF of Escherichia coli, the antibiotic interacts with two binding sites within the pore, thus partially blocking the ionic current. The modulation of one affinity site by Mg(2+) reveals further details of binding sites and binding kinetics. At positive membrane potentials, the slow blocking events induced by enrofloxacin in Mg(2+)-free media are converted to flickery sojourns at the highest apparent current level (all three pores flickering). This indicates weaker binding in the presence of Mg(2+). Analysis of the resulting amplitude histograms with β distributions revealed the rate constants of blocking (k(OB)) and unblocking (k(BO)) in the range of 1,000 to 120,000 s(-1). As expected for a bimolecular reaction, k(OB) was proportional to blocker concentration and k(BO) independent of it. k(OB) was approximately three times lower for enrofloxacin coming from the cis side than from the trans side. The block was not complete, leading to a residual conductivity of the blocked state being ∼25% of that of the open state. Interpretation of the results has led to the following model: fast flickering as caused by interaction of Mg(2+) and enrofloxacin is related to the binding site at the trans side, whereas the cis site mediates slow blocking events which are also found without Mg(2+). The difference in the accessibility of the binding sites also explains the dependency of k(OB) on the side of enrofloxacin addition and yields a means of determining the most plausible orientation of OmpF in the bilayer. The voltage dependence suggests that the dipole of the antibiotic has to be adequately oriented to facilitate binding.

Fast gating of ion channels with rate constants higher than the corner frequency of the recording set-up can be evaluated by fitting so-called beta distributions to measured amplitude histograms. Up to now, this was preferentially done for O-C Markov sub-models with one open and one closed state. Here, a fit of the amplitude histograms from MaxiK (BK) single-channel records was achieved with a five-state model with two open and three closed states including three open-close transitions with rate constants higher than the corner frequency (20 kHz) of the inevitable low-pass filter of the recording system. The numerical values of the rate constants of these transitions enabled a nearly one-to-one relationship between typical regions of the histograms and the reactions in the Markov model. These characteristic features are the width of the peak at the apparent single-channel current, the side slopes at the open and at the closed peak, and the depth of the valley between the two peaks. However, the simplex routine alone was incapable of finding the solution but could do so if guided by hand along a suggested strategy.

Kcv from the chlorella virus PBCV-1 is a viral protein that forms a tetrameric, functional K+ channel in heterologous systems. Kcv can serve as a model system to study and manipulate basic properties of the K+ channel pore because its minimalistic structure (94 amino acids) produces basic features of ion channels, such as selectivity, gating, and sensitivity to blockers. We present a characterization of Kcv properties at the single-channel level. In symmetric 100 mM K+, single-channel conductance is 114+/-11 pS. Two different voltage-dependent mechanisms are responsible for the gating of Kcv. "Fast" gating, analyzed by beta distributions, is responsible for the negative slope conductance in the single-channel current-voltage curve at extreme potentials, like in MaxiK potassium channels, and can be explained by depletion-aggravated instability of the filter region. The presence of a "slow" gating is revealed by the very low (in the order of 1-4%) mean open probability that is voltage dependent and underlies the time-dependent component of the macroscopic current.

Microsecond gating of ion channels can be evaluated by fitting beta distributions to amplitude histograms of measured time series. The shape of these histograms is determined not only by the rate constants of the gating process (in relation to the filter frequency) but also by baseline noise and shot noise, resulting from the stochastic nature of ion flow. Under normal temporal resolution, the small shot noise can be ignored. This simplification may no longer be legitimate when rate constants reach the range above 1 mus(-1). Here, the influence of shot noise is studied by means of simulated time series for several values of single-channel current of the fully open state and baseline noise. Under realistic optimal conditions (16 pA current, 1 pA noise, 50 kHz bandwidth), ignoring the shot noise leads to an underestimation of the rate constants above 1 mus(-1) by a factor of about 2.5. However, in that range, the scatter of the evaluated rate constants is at least of the same magnitude, obscuring the systematic error. The incorporation of shot noise into the analysis will become more important when amplifiers with significantly reduced noise become available.

Basic principles of the gating mechanisms of neuronal sodium channels, especially the fast inactivation process, were revealed by a quantitative analysis of the effects of the chemically irreversible modifying agent chloramine T. The compound is known to enhance the open probability of sodium channels by interfering with the inactivation process. The key for the deduction of structure-function relationships was obtained from the analysis of single-channel patch-clamp data, especially the finding that chloramine T-induced modification of inactivation occurred in four steps. These steps were termed modes 1-4 (four-mode gating model), and their temporal sequence was always the same. The kinetic analysis of single-channel traces with an improved two-dimensional dwell-time fit revealed the possible mechanism related to each mode. Similarities to the kinetics of the sodium channel mutant F1489Q led to the assignment of modes 1 and 2 to transient defects in the locking of the inactivation particle (hinged lid). In the third mode, the hinged lid was unable to lock permanently. Finally, in mode 4, the apparent single-channel current was reduced, which could be explained by fast gating, presumably related to the selectivity filter.

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed at high temporal resolution (50-kHz filter) in asymmetrical solutions containing 0, 25, 50, or 150 mM Tl+ on the luminal or cytosolic side with [K+] + [Tl+] = 150 mM and 150 mM K+ on the other side. Outward current in the presence of cytosolic Tl+ did not show fast gating behavior that was significantly different from that in the absence of Tl+. With luminal Tl+ and at membrane potentials more negative than -40 mV, the single-channel current showed a negative slope resistance concomitantly with a flickery block, resulting in an artificially reduced apparent single-channel current I(app). The analysis of the amplitude histograms by beta distributions enabled the estimation of the true single-channel current and the determination of the rate constants of a simple two-state O-C Markov model for the gating in the bursts. The voltage dependence of the gating ratio R = I(true)/I(app) = (k(CO) + k(OC))/k(CO) could be described by exponential functions with different characteristic voltages above or below 50 mM Tl(+). The true single-channel current I(true) decreased with Tl+ concentrations up to 50 mM and stayed constant thereafter. Different models were considered. The most likely ones related the exponential increase of the gating ratio to ion depletion at the luminal side of the selectivity filter, whereas the influence of [Tl+] on the characteristic voltage of these exponential functions and of the value of I(true) were determined by [Tl+] at the inner side of the selectivity filter or in the cavity.

The demonstrated modified spectrophotometric method makes use of the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical and its specific absorbance properties. Theabsorbance decreases when the radical is reduced by antioxidants. In contrast to otherinvestigations, the absorbance was measured at a wavelength of 550 nm. This wavelengthenabled the measurements of the stable free DPPH radical without interference frommicroalgal pigments. This approach was applied to methanolic microalgae extracts for twodifferent DPPH concentrations. The changes in absorbance measured vs. the concentrationof the methanolic extract resulted in curves with a linear decrease ending in a saturationregion. Linear regression analysis of the linear part of DPPH reduction versus extractconcentration enabled the determination of the microalgae's methanolic extractsantioxidative potentials which was independent to the employed DPPH concentrations. Theresulting slopes showed significant differences (6 - 34 μmol DPPH g -1 extractconcentration) between the single different species of microalgae (Anabaena sp.,Isochrysis galbana, Phaeodactylum tricornutum, Porphyridium purpureum, Synechocystissp. PCC6803) in their ability to reduce the DPPH radical. The independency of the signal on the DPPH concentration is a valuable advantage over the determination of the EC50 value.

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed with a high temporal resolution (50-kHz filter) in symmetrical solutions with 50, 150, or 400 mM KCl and 2.5 mM CaCl(2) and 2.5 mM MgCl(2). At membrane potentials >+100 mV, the single-channel current showed a negative slope resistance, concomitantly with a flickery block, which was not influenced by Ca(2+) or Mg(2+). The analysis of the amplitude histograms by beta distributions revealed that current in this voltage range was reduced by two effects: rate limitation at the cytosolic side of the pore and gating with rate constants 10-20-fold higher than the cutoff frequency of the filter (i.e., dwell times in the microsecond range). The data were analyzed in terms of a model that postulates a coupling between both effects; if the voltage over the selectivity filter withdraws ions from the cavity at a higher rate than that of refilling from the cytosol, the selectivity filter becomes instable because of ion depletion, and current is interrupted by the resulting flickering. The fit of the IV curves revealed a characteristic voltage of 35 mV. In contrast, the voltage dependence of the gating factor R, i.e., the ratio between true and apparent single-channel current, could be fitted by exponentials with a characteristic voltage of 60 mV, suggesting that only part of the transmembrane potential is felt by the flux through the selectivity filter.

Measuring chlorophyll fluorescence at five different wavelengths provides the discrimination of four phytoplankton groups. Here the problems associated with a free-falling depth profiler for phytoplankton discrimination are considered. When F0, F, and Fm are determined sequentially in the same measuring cell, then the algae inside the cell have a different light history. It depends on their different locations in the cell as caused by the induction curve of chlorophyll fluorescence. Mathematical algorithms are developed which enable the calculation of the concentrations of individual phytoplankton groups from the integral fluorescence signal (averaged for 1s) for different velocities of the falling probe. The theory requires the knowledge of the fluorescence behaviour of phytoplankton in stationary suspensions. The predictions of the model are compared with measurements in flowing suspensions containing chlorophyta, cyanobacteria, cryptophyta and diatoms. The comparison shows the reliability of the algorithms. The application of the algorithms is indispensable for dark-adapted cells and is less important for light-adapted cells.

Single-channel current seems to be one of the most obvious characteristics of ion transport. But in some cases, its determination is more complex than anticipated at first glance. Problems arise from fast gating in time series of patch-clamp current, which can lead to a reduced apparent (measured) single-channel current. Reduction is caused by undetected averaging over closed and open intervals in the anti-aliasing filter. Here it is shown that fitting the measured amplitude histograms by Beta distributions is an efficient tool of reconstructing the true current level from measured data. This approach becomes even more powerful when it is applied to amplitude distributions-per-level. Simulated time series are employed to show that the error sum is a good guideline for finding the correct current level. Furthermore, they show that a Markov model smaller than the one used for gating analysis can be used for current determination (mostly O-C, i.e., open-closed). This increases the reliability of the Beta fit. The knowledge of the true current level is not only important for the understanding of the biophysical properties of the channel. It is also a prerequisite for the correct determination of the rate constants of gating. The approach is applied to measured data. The examples reveal the limits of the analysis imposed by the signal-to-noise ratio and the shape of the amplitude distribution. One application shows that the negative slope of the I-V curve of the human MaxiK channel expressed in HEK293 cells is caused by fast gating.

Two-dimensional (2D) dwell-time analysis of time series of single-channel patch-clamp current was improved by employing a Hinkley detector for jump detection, introducing a genetic fit algorithm, replacing maximum likelihood by a least square criterion, averaging over a field of 9 or 25 bins in the 2D plane and normalizing per measuring time, not per events. Using simulated time series for the generation of the "theoretical" 2D histograms from assumed Markov models enabled the incorporation of the measured filter response and noise. The effects of these improvements were tested with respect to the temporal resolution, accuracy of the determination of the rate constants of the Markov model, sensitivity to noise and requirement of open time and length of the time series. The 2D fit was better than the classical hidden Markov model (HMM) fit in all tested fields. The temporal resolution of the two most efficient algorithms, the 2D fit and the subsequent HMM/beta fit, enabled the determination of rate constants 10 times faster than the corner frequency of the low-pass filter. The 2D fit was much less sensitive to noise. The requirement of computing time is a problem of the 2D fit (100 times that of the HMM fit) but can now be handled by personal computers. The studies revealed a fringe benefit of 2D analysis: it can reveal the "true" single-channel current when the filter has reduced the apparent current level by averaging over undetected fast gating.

5-(and-6)-Carboxy-2',7'-dichlorodihydrofluorescein diacetate (DCF-DA), a permeative indicator of oxidative stress, was loaded into dissected leaves of wheat in order to monitor the temporal development of reactive oxygen species. DCF fluorescence was found to be constant under dark conditions. Upon loading the leaves with salicyl hydroxamate, a blocker of the alternative oxidase, DCF fluorescence linearly increased in the dark. This indicates a function of alternative oxidase in preventing reactive oxygen radicals in the mitochondria. Upon illumination, the DCF signal decreased within 5 min. As illuminated chloroplasts would increase the load of reactive oxygen species, the observed decrease cannot be assigned to the production of reactive oxygen species in the chloroplasts. Three different putative mechanisms are considered which all assign an important role to light-induced delivery of NAD(P)H: (1) direct quenching of DCF fluorescence by light-generated NAD(P)H, (2) light-stimulated activation of scavenging enzymes, or (3) redirection of mitochondrial electron fluxes as caused by the delivery of excess redox equivalents (NADH) from the chloroplasts.

Light-induced generation of reactive oxygen species (ROS) in 2-week-old leaves of Arabidopsis thaliana was studied by means of the ROS-sensitive dyes nitroblue tetrazolium (NBT) and 5-(and-6)-carboxy-2',7'-dichlorodihydrofluorescein diacetate (DCF-DA). Superposition of pictures of chlorophyll fluorescence and DCF fluorescence indicated that the origin of ROS was in the chloroplasts. Experiments were done with zero, 0.1, or 10 mM NaHCO3 in the infiltration medium. Energy quenching in photosystem II was higher under low CO2 concentrations as measured by chlorophyll fluorescence. DCF fluorescence showed that CO2 deficiency led to an increase of ROS generation. In contrast, the photosystem II inhibitor 3-(3,4-dichlorophenyl)-1,1-dimethylurea reduced the light-induced increase of DCF fluorescence. This indicates that ROS production does not primarily result from over-reduction of photosystem II as caused by impeding electron flow in the electron transfer chain. More likely, it is an effect of diverting electron flux normally aimed at carboxylation in the Calvin cycle to other sinks more prone to the generation of toxic radicals. There was no significant effect of salicyl hydroxamate (a blocker of the alternative oxidase), showing that the mitochondrial electron transfer chain seems to play a minor role as already indicated by the superposition of chlorophyll and DCF fluorescence.

Fast gating in time series of patch-clamp current demands powerful tools to reveal the rate constants of the adequate Hidden Markov model. Here, two approaches are presented to improve the temporal resolution of the direct fit of the time series. First, the prediction algorithm is extended to include intermediate currents between the nominal levels as caused by the anti-aliasing filter. This approach can reveal rate constants that are about 4 times higher than the corner frequency of the anti-aliasing filter. However, this approach is restricted to time series with very low noise. Second, the direct fit of the time series is combined with a beta fit, i.e., a fit of the deviations of the amplitude histogram from the Gaussian distribution. Since the "theoretical" amplitude histograms for higher-order Bessel filters cannot be calculated by analytical tools, they are generated from simulated time series. In a first approach, a simultaneous fit of the time series and of the Beta fit is tested. This simultaneous fit, however, inherits the drawbacks of both approaches, not the benefits. More successful is a subsequent fit: The fit of the time series yields a set of rate constants. The subsequent Beta fit uses the slow rate constants of the fit of the time series as fixed parameters and the optimization algorithm is restricted to the fast ones. The efficiency of this approach is illustrated by means of time series obtained from simulation and from the dominant K+ channel in Chara. This shows that temporal resolution can reach the microsecond range.

Level or jump detectors generate the reconstructed time series from a noisy record of patch-clamp current. The reconstructed time series is used to create dwell-time histograms for the kinetic analysis of the Markov model of the investigated ion channel. It is shown here that some additional lines in the software of such a detector can provide a powerful new means of patch-clamp analysis. For each current level that can be recognized by the detector, an array is declared. The new software assigns every data point of the original time series to the array that belongs to the actual state of the detector. From the data sets in these arrays distributions-per-level are generated. Simulated and experimental time series analyzed by Hinkley detectors are used to demonstrate the benefits of these distributions-per-level. First, they can serve as a test of the reliability of jump and level detectors. Second, they can reveal beta distributions as resulting from fast gating that would usually be hidden in the overall amplitude histogram. Probably the most valuable feature is that the malfunctions of the Hinkley detectors turn out to depend on the Markov model of the ion channel. Thus, the errors revealed by the distributions-per-level can be used to distinguish between different putative Markov models of the measured time series.

Fluorometric determination of the chlorophyll (Chl) content of cyanobacteria is impeded by the unique structure of their photosynthetic apparatus, i.e., the phycobilisomes (PBSs) in the light-harvesting antennae. The problems are caused by the variations in the ratio of the pigment PC to Chl a resulting from adaptation to varying environmental conditions. In order to include cyanobacteria in fluorometric analysis of algae, a simplified energy distribution model describing energy pathways in the cyanobacterial photosynthetic apparatus was conceptualized. Two sets of mathematical equations were derived from this model and tested. Fluorescence of cyanobacteria was measured with a new fluorometer at seven excitation wavelength ranges and at three detection channels (650, 685 and 720 nm) in vivo. By employing a new fit procedure, we were able to correct for variations in the cyanobacterial fluorescence excitation spectra and to account for other phytoplankton signals. The effect of energy-state transitions on the PC fluorescence emission of PBSs was documented. The additional use of the PC fluorescence signal in combination with our recently developed mathematical approach for phytoplankton analysis based on Chl fluorescence spectroscopy allows a more detailed study of cyanobacteria and other phytoplankton in vivo and in situ.

The dependence of single-channel current on the Tl+/K+ mole fraction exhibiting a minimum at [Tl+]/[K+] of about 1:15 is proportional to open probability in bursts. Five models are suggested to explain modulation of gating by the Tl+/K+ ratio. Three models start from a channel with 4 identical subunits, each with an allosteric binding site for K+ or Tl+. In the first model, ion binding is directly observable as a transition from one Markov state to another. This model can explain the dependence of the apparent single-channel current on Tl+ concentrations. However, the predicted linear dependence on ion concentrations of the apparent rate constants was not observed in measurements in 25 or 250 mM KNO3 and 250 mM Tl NO3. The second model can overcome this problem by introducing saturation kinetics for ion binding. In the third model, gating is caused by inherent vibrations of the protein, and the rate constants of the related transitions depend on the occupation of the allosteric sites. The fourth model is based on the foot-in-the-door approach with the essential feature that two K+ ions in the selectivity filter are necessary to keep the pore radius suitable for K+ ions. The fifth model is also a foot-in-the-door model, but non-Markovian because, similar to model 3, it is assumed that the conformation of the protein (and thus the rate constants of the Markov model of the time series) depends on the force exerted by the temporal average over the states of a Markov model of ion occupation. These ions may reside in the pore itself or outside.

The algorithm proposed here for automatic level detection in noisy time series of patch-clamp current is based on the detection of jump-free sections in the time series. The detector moves along the time series and uses a chi(2) test for the detection of jumps. When a jump is detected, the mean value, the variance and the length of the preceding jump-free section are stored. A Student's t-test was employed for the assignment of detected jump-free sections to discrete levels of the Markov model and for rejection of all sections with multiple assignments. The choice of the two significance levels is based on a 3-D diagram displaying the average number of detected levels from several time series vs. the significance levels of jump detection and of level assignment. The correct one is selected out of several plateaus with integer number of levels by means of the criterion of minimum scatter or other plausibility considerations. The test has been applied to simulated data obtained from a 2-state model and a 5-state aggregated Markov model, and the influences of SNR and of gating frequency are shown. Finally, the performance of the level detector is compared with a fit-by-eye and with a fit of the amplitude histogram by a sum of gaussians. At high noise, the fit of amplitude histograms failed, whereas the other two approaches were about equal.

Fingerprints of excitation spectra of chlorophyll (Chl) fluorescence can be used to differentiate 'spectral groups' of microalgae in vivo and in situ in, for example, vertical profiles within a few seconds. The investigated spectral groups of algae (green group, Chlorophyta; blue, Cyanobacteria; brown, Heterokontophyta, Haptophyta, Dinophyta; mixed, Cryptophyta) are each characterised by a specific composition of photosynthetic antenna pigments and, consequently, by a specific excitation spectrum of the Chl fluorescence. Particularly relevant are Chl a, Chl c, phycocyanobilin, phycoerythrobilin, fucoxanthin and peridinin. A laboratory-based instrument and a submersible instrument were constructed containing light-emitting diodes to excite Chl fluorescence in five distinct wavelength ranges. Norm spectra were determined for the four spectral algal groups (several species per group). Using these norm spectra and the actual five-point excitation spectrum of a water sample, a separate estimate of the respective Chl concentration is rapidly obtained for each algal group. The results of dilution experiments are presented. In vivo and in situ measurements are compared with results obtained by HPLC analysis. Depth profiles of the distribution of spectral algal groups taken over a time period of few seconds are shown. The method for algae differentiation described here opens up new research areas, monitoring and supervision tasks related to photosynthetic primary production in aquatic environments.

A chi(2) test is proposed that provides a means of discriminating between different Markov models used for the description of a measured (patch clamp) time series. It is based on a test statistic constructed from the measured and the predicted number of transitions between the current levels. With a certain probability, this test statistic is below a threshold if the model with a reduced number of degrees of freedom is compatible with the data. A second criterion is provided by the dependence of the test statistic on the number of data points. For data generated by the alternative model it increases linearly. The applicability of this test for verifying and rejecting models is illustrated by means of time series generated by two distinct channels with different conductances and by time series generated by one channel with two conductance levels. For noisy data, a noise correction is proposed, which eliminates noise-induced false jumps that would interfere with the test. It is shown that the test can also be extended to aggregated Markov models.

Rb(+) as a tracer for K(+) was used to test the hypothesis that uptake of K(+) from xylem vessels of small veins into the symplast of maize leaves occurs at the xylem/bundle sheath cell interface. 22.5 min after immersing cut leaves into 20 mM RbCl+1 mM KCl, Rb(+) appeared in the cells of the leaves. Sections of these leaves were freeze-dried. In cryo-thin sections (5 microm), (85)Rb(+) and (41)K(+) content was determined by laser microprobe mass analysis with a large resolution of about 1 microm. Determining the ratio of (85)Rb(+) to (41)K(+) in the cell walls and cytosols of bundle sheath cells, mesophyll cells, and in the cells between the xylem elements resulted in the following picture: In small veins, Rb(+) entered the symplast directly at the xylem/bundle sheath cell interface.

The anomalous mole fraction effect (AMFE) of the K(+) channel in excised patches of the tonoplast of Chara showed a minimum of apparent open-channel current at 20 mM Tl(+) and 230 mM K(+). Time series obtained at a sampling rate of 100 kHz (filter 25 kHz) were analyzed by three methods to find out whether the AMFE results from an effect on gating or on the conductivity of the open state. Fitting the amplitude histograms by a superposition of gaussians showed a broadening in the presence of Tl(+). Dwell-time analysis based on an O-O-C-C-C model failed to evaluate rate constants above the filter frequency. Thus, the absence of any reduction of apparent open-channel current in time series simulated with the evaluated rate constants could not be taken as evidence against the hypothesis of gating. Finally, a direct fit of the measured time series using five different 5-state Hidden Markov models revealed that the presence of Tl(+) changed the rate constants in such a way that the number of transitions into the short-lived open state (30 micros) increased strongly compared to those in the absence of Tl(+). These models explain 25% reduction of apparent single-channel current amplitude through a rapid gating mechanism.

The isolation of bundle sheath protoplasts from leaves of Zea mays L. for patch clamp whole-cell experiments presents special problems caused by the suberin layer surrounding these cells. These problems were overcome by the isolation technique described here. Two different types of whole-cell response were found: a small response caused by MB-1 (maize bundle sheath conductance type 1) which was instantaneously activated, and another caused by MB-2 (maize bundle sheath conductance type 2) consisting of an instantaneous response (maize bundle sheath K+ instantaneous current type 2; MB-KI2) similar to but stronger than the current through MB-1 plus a small time-dependent outward rectifying component (maize bundle sheath activated outward rectifying current; MB-AOR) with voltage-dependent delayed activation. The occurrence of MB-AOR was often accompanied by a smaller contribution from an inward rectifying channel at negative potentials. Activation of MB-2 required ATP. It is suggested that MB-1 and MB-2 are related to bundle sheath cells with and without direct contact with the xylem vessels. In mesophyll cells, only one type of response caused by MM-2 (maize mesophyll conductance type 2) was found with an instantaneous (maize mesophyll K+ instantaneous current type 2, MM-KI2) and a voltage-dependent delayed component (maize mesophyll activated outward rectifying current, MM-AOR). The most striking difference between bundle sheath and mesophyll cells was the pH dependence of K+ uptake. At pH 7.2, uptake of K+ by MB-2 was identical to that by MM-2 over the whole voltage range. However, acidification stimulated K+ conductance in bundle sheath cells, whereas a decrease was found for MM-2. At pH 6.15, the bundle sheath channel MB-2 had more than a 10-fold higher K+ uptake at positive and negative potentials than MM-2. The channel MB-1, too, was stimulated by low pH. This seems to indicate a putative role for MB-1 and MB-2 in charge balance during uptake of nutrients via cotransport from the xylem into the symplasm.

Fluorescence clamp (FC) is a method of directly measuring the fluxes out of Photosystem II antenna. This is achieved by a feed-back loop which controls the light intensity of light emitting diodes in order to keep the amplitude of modulated chlorophyll fluorescence constant, and by taking the intensity or the current fed into the light emitting diodes as a measure of the fluxes. Saturating flashes serve to distinguish between fluxes into thermal deactivation and into the photosynthetic electron transfer chain (ETC). As FC is only active in the light period of the measuring light, the background signal (induced by actinic light) is compensated by a second feed-back loop in the dark period of the measuring light. Equations are provided for the interpretation of the FC signals. This includes the quenching parameters of chlorophyll fluorescence, the flux into the electron transfer chain and the redox state of Q(A). Experiments are presented which show that traditional fluorescence (LC) and FC measurements yield the same results. However, the FC method provides a better presentation of fluxes as the scaling factor (flux/signal) is constant for all states of Photosystem II. This leads to a simpler analysis of quenching mechanisms. Examples are given which show that the co-existing quenching mechanisms with different effects on photochemical and non-photochemical fluxes can be better identified by FC rather than by LC.

Aluminium, the most abundant metal in the earth's crust, is highly toxic to most plant species. One of the prevailing dogmas is that aluminium exerts this effect by disrupting cellular calcium homeostasis. However, recent research gives strongly conflicting results: aluminium was shown to provoke either an increase or a decrease in cytosolic free calcium concentration ([Ca2+]c). To solve this question, we have adopted a novel approach: [Ca2+]c measurements in intact plant roots as opposed to isolated cells, and the correlative measurements of intracellular and external pH. The results obtained show that plant roots respond to low external pH by a sustained elevation in [Ca2+]c. In the presence of aluminium, this pH-mediated elevation in [Ca2+]c does not occur, therefore any potential calcium-mediated protection against low pH is likely to be irreversibly inhibited. The severity of the inhibitory effect of aluminium on [Ca2+]c depends on the concentration of external calcium, thus perhaps explaining why the effects of aluminium toxicity are ameliorated in calcium-rich soils. It seems possible that a primary toxic effect of aluminium might be to impair calcium-mediated plant defence responses against low pH.

Cold elicits an immediate rise in the cytosolic free calcium concentration ([Ca2+]c) of plant cells. We have studied the concerted action of the three underlying mechanisms, namely sensing, sensitisation and desensitisation, which become important when plants in the field are subjected to changes in temperature. We applied different regimes of temperature changes with well-defined cooling rates to intact roots of Arabidopsis thaliana expressing the calcium-indicator, aequorin. Our results indicate that temperature sensing is mainly dependent on the cooling rate, dT/dt, whereas the absolute temperature T is of less importance. Arabidopsis roots were found to be sensitive to cooling rates of less than dT/dt = 0.01 degrees C/s. However, at cooling rates below 0.003 degrees C/s (i.e. cooling 10 degrees C in 1 h) there is no detectable [Ca2+]c response at all. At low temperature, the sensitivity of the plant cold-detection system is increased. This in turn produces greater cooling-induced [Ca2+]c elevations. Prolonged or repeated cold treatment attenuates the [Ca2+]c responses to subsequent episodes of cooling.

The divalent cation Sr2+ induced repetitive transient spikes of the cytosolic Ca2+ activity [Ca2+]cy and parallel repetitive transient hyperpolarizations of the plasma membrane in the unicellular green alga Eremosphaera viridis. [Ca2+]cy measurements, membrane potential measurements, and cation analysis of the cells were used to elucidate the mechanism of Sr2+-induced [Ca2+]cy oscillations. Sr2+ was effectively and rapidly compartmentalized within the cell, probably into the vacuole. The [Ca2+]cy oscillations cause membrane potential oscillations, and not the reverse. The endoplasmic reticulum (ER) Ca2+-ATPase blockers 2,5-di-tert-butylhydroquinone and cyclopiazonic acid inhibited Sr2+-induced repetitive [Ca2+]cy spikes, whereas the compartmentalization of Sr2+ was not influenced. A repetitive Ca2+ release and Ca2+ re-uptake by the ER probably generated repetitive [Ca2+]cy spikes in E. viridis in the presence of Sr2+. The inhibitory effect of ruthenium red and ryanodine indicated that the Sr2+-induced Ca2+ release from the ER was mediated by a ryanodine/cyclic ADP-ribose type of Ca2+ channel. The blockage of Sr2+-induced repetitive [Ca2+]cy spikes by La3+ or Gd3+ indicated the necessity of a certain influx of divalent cations for sustained [Ca2+]cy oscillations. Based on these data we present a mathematical model that describes the baseline spiking [Ca2+]cy oscillations in E. viridis.

Cytosolic Ca2+ activity ([Ca2+]cy) and membrane potential were measured simultaneously in the unicellular green alga Eremosphaera viridis. Steady state [Ca2+]cy was about 160 nM. A 'light-off' stimulus induced a transient elevation of [Ca2+]cy ([Ca2+]cy spike) in parallel with a transient hyperpolarization of the plasma membrane. Caffeine and Sr2+, known to release Ca2+ from intracellular stores in animal cells, induced repetitive [Ca2+]cy spikes in Eremosphaera which were always accompanied by parallel repetitive transient hyperpolarizations. These transient hyperpolarizations could be used as an indicator for [Ca2+]cy spikes. Repetitive [Ca2+]cy spikes in Eremosphaera were similar to repetitive [Ca2+]cy spikes in excitable animal cells. The mechanisms underlying these [Ca2+]cy oscillations seem to be comparable in animal and plant cells.

Models of different level are applied to plant membrane transport. For the evaluation of I/V curves, models based on enzyme kinetics, limitation by diffusion and the ion well are described. Physical models of ion-ion interaction deal with the Woodhull model, the multi-site single-file ion pore, the ion-ion ion-water interaction model and the effect of screening. The discussion of channel gating starts with pre-patch evidence of gating and the biological importance of gating. State models play a dominant role in the analysis of patch clamp records. Gating may strongly interfere with permeation models. With respect to this, the limits of temporal resolution are of great importance. The effects of Na(+) and Tl(+) are examples of the influence of fast gating on modelling and the problems of its detection. The highest level of modelling is achieved when the knowledge about the structure of channels is employed for the modelling of gating. Major topics in this field are blockade by ions and phosphorylation.

The maximum-likelihood technique for the direct estimation of rate constants from the measured patch clamp current is extended to the analysis of multi-channel recordings, including channels with subconductance levels. The algorithm utilizes a simplified approach for the calculation of the matrix exponentials of the probability matrix from the rate constants of the Markov model of the involved channel(s) by making use of the Kronecker sum and product. The extension to multi-channel analysis is tested by the application to simulated data. For these tests, three different channel models were selected: a two-state model, a three-state model with two open states of different conductance, and a three-state model with two closed states. For the simulations, time series of these models were calculated from the related first-order, finite-state, continuous-time Markov processes. Blue background noise was added, and the signals were filtered by a digital filter similar to the anti-aliasing low-pass. The tests showed that the fit algorithm revealed good estimates of the original rate constants from time series of simulated records with up to four independent and identical channels even in the case of signal-to-noise ratios being as low as 2. The number of channels in a record can be determined from the dependence of the likelihood on channel number. For large enough data sets, it takes on a maximum when the assumed channel number is equal to the "true" channel number.

The Cs+ block of K+ channels has often been investigated by methods that allow only indirect estimation of the rate constants of blocking and re-opening. This paper presents single-channel records with high temporal resolution which make the direct observation of the fast transitions between the blocked and the unblocked state possible. The rate constants kOGb, kGbO of Cs(+)-dependent blocking and of re-opening are evaluated from the time constants found in the open-time and closed-time histograms. The blocking rate constant kOGb between 1000 and 50000 s-1 depends linearly on the Cs+ concentration and strongly on voltage, increasing by a factor of 1.44 per 10 mV hyperpolarization. The re-opening rate constant kGbO approximately 30000 s-1 is independent of Cs+ concentration and only slightly voltage-dependent. Formally, the results can be described by a Woodhull-model. The strong voltage dependence with d > 1, however, weakens its plausibility. The results are interpreted in terms of a molecular framework emerging from recent results on the structure of voltage-gated channels.

Spontaneous cooperatively of K+ channels is studied in excised patches of Chara corallina tonoplasts. Bar histograms (dwell time versus number of open channels) are constructed from the time series of current by means of the higher-order Hinkley detector (R. Schultze and S. Draber. 1993. J. Membr. Biol. 132:41-52). A statistical test, based on these bar histograms, shows that the channels are not independent. Further analysis reveals that the channels are cooperatively changing their open probability, which leads to the idea of cooperative mode shifting.

Schreiber and Neubauer (Photosynthesis Research 25: 279-293, 1990) have proposed a model which explains energy quenching by enhanced triplet formation as caused by charge recombination due to pH-dependent donor-side limitation. Quenching under these conditions is assumed to result from two mechanisms. Firstly, there is the withdrawal of excited states by charge recombination and formation of triplet states. Secondly, these triplet states can result in carotenoid triplets in the antenna which are supposed to quench excitons. Here, it is shown that quenching caused by both mechanisms can account for only about 25% of the experimentally observed energy quenching even under extremely favorable conditions. More likely, this number is less than 15%, as the contribution of the second step in the proposed triplet cycle is expected to be low as the life times of the carotenoid triplets are not long enough to cause the assumed quenching of excitons in the antenna.

Laser-velocimetry was applied in order to study the effect of light on the velocity of protoplasmic streaming (pps) in Characean cells. A change from dark to light (= 6 W · m(-2)) leads to an acceleration of streaming by about 15-30% with a time-constant of approx. 300 s. The transition from light to dark causes a transient decrease of velocity below the original dark level. This response occurs with a time constant of about 500 s. It returns to its initial value with a time-constant of about 2000 s. This may indicate that a control loop of cytosolic homeostasis takes a decrease in pCa more seriously than an increase. A possible involvement of temperature effects caused by illumination was excluded by measuring the influence of temperature. Steady-state velocity of streaming changed by 5% per 1° C. Irradiation with infra-red light (λ > 780 nm) did not cause a change in velocity. The absence of a light effect on streaming velocity in the presence of 3-(3',4'-dichlorophenyl)-1,1-dimethylurea (DCMU) shows that photosynthesis and not phytochrome is involved. The role of light-induced changes of pCa is discussed, especially with respect to the hypothesis of Vanselow and Hansen (1989, J. Membr. Biol. 110, 175-187) that photosynthesis acts on the plasmalemma K(+)-channel via light-induced uptake of Ca(2+) into the chloroplasts.

Biophysical and numerical analysis methods were used to characterize and model the transport protein that gives rise to the acid and alkaline regions of Chara. A measuring system that permits the detection of area-specific current-voltage curves was used. These current-voltage curves, obtained from the inward current regions of Chara, underwent a parallel shift when the alkaline region was inverted by means of an acid pH treatment. In this situation the reversal potential of this area shifted from -120 mV to -340 mV. Together with data obtained from experiments using a divided chamber system, these results suggest that a common transport protein generates inward and outward current regions of Chara. On the basis of these experimental findings, a reaction kinetic model is proposed that assigns two operational modes to the proposed transport protein. Switching between these modes generates either acid or alkaline behavior. Since the observed pH dependence of the postulated transporter is rather complex, a reaction kinetic saturation mechanism had to be incorporated into the model. This final 10-state reaction kinetic model provides an appropriate set of mathematical relations to fit the measured current-voltage curves by computer.

Patch-clamp studies have been employed in order to check whether the assumption of a multi-ion single-file pore is necessary for the explanation of the anomalous mole fraction effect or whether this effect can also be explained by a single-barrier enzyme kinetic model. Experiments in the cell-attached configuration were done on the tonoplast membrane of cytoplasmic droplets of Nitella in solutions containing 150 mol m-3 of K+ plus Tl+ with seven different K+/Tl+ ratios. At first sight, the results seem to support the multi-ion single-file pore, because apparent open channel conductivity displays the anomalous mole fraction effect, whereas open-probability has not been found to be dependent on the K+/Tl+ ratio. Changes in open probability would be expected for a single-barrier enzyme kinetic model with a lazy state. On the other hand, the lazy-state model is more successful in explaining the measured I-V curves. The entire slope of the apparent open channel current-voltage curves rotates with changing K+/Tl+ ratios in the whole voltage range between -100 and +80 mV. Numerical calculations on the basis of multi-ion single-file pores could create the anomalous mole fraction effect only in a limited voltage range with intersecting I-V curves. The apparent absence of an effect on open probability which is postulated by the lazy-state model can be explained if switching into and out of the lazy state is faster than can be resolved by the temporal resolution of 1 msec.

The investigation of the kinetics of chlorophyll-fluorescence under continuous background light enables the application of linearizing conditions. This approach, which provides a quantitative evaluation by means of curve-fitting routines, is applied to the investigation of the linear kinetics of the I-D-P phase. Using changes in PS II-light, PS I-light and in CO2-concentration as input signals showed that a pool at the acceptor side of PS I, in addition to the plastoquinone pool, plays an essential role in the generation of the dip. The occurrence of the dip is related to the sign of the faster one of the two components related to the I-D and the D-P phase. This sign can be inverted by the ratio of PS I and PS II light. However, model calculations show that the change of this sign does not allow a decision which one of the two components is related to which one of the two pools. The dependence of the sign of the faster component on light conditions can generate different types of I-D-P transitions, namely nearly monophasic increases, sigmoid responses or dips. As these phenomena are already created by the linear responses, non-linear effects or additional loops between PS II and PS I are not required for the explanation of the basic features.

The mechanism of energy-dependent quenching (qE) of chlorophyll fluorescence was studied employing photoacoustic measurements of oxygen evolution and heat release. It is shown that concomitant to the formation of qE the yield of open reaction centers φp decreases indicating that qE quenching originates from a process being competitive to fluorescence as well as to photochemistry. The analysis of heat release (rate of thermal deactivation) shows: 1. The competitive process is not given by a still unknown energy storing process. 2. If the competitive process would be a futile cycle the life-times of the involved intermediates had to be faster than 50 μs.The results of the photoacoustic measurements are in line with the idea that qE quenching originates from an increased probability of thermal deactivation of excited chlorophylls.

Reaction kinetic analysis of the electrical properties of the electrogenic Cl(-) pump inAcetabularia has been extended from steady-state to nonsteady-state conditions: electrical frequency responses of theAcetabularia membrane have been measured over the range from 1 Hz to 10 kHz at transmembrane potential differences across the plasmalemma (V m ) between -70 and -240 mV using voltage-clamp techniques. The results are well described by an electrical equivalent circuit with three parallel limbs: a conventional membrane capacitancec m , a steadystate conductanceg o (predominantly of the pump pathway plus a minor passive ion conductance) and a conductanceg s in series with a capacitancec p which are peculiar to the temporal behavior of the pump. The absolute values and voltage sensitivities of these four elements have been determined:c m of about 8 mF m(-2) turned out to be voltage insensitive; it is considered to be normal.g o is voltage sensitive and displays a peak of about 80 S m(-2) around -180 mV. Voltage sensitivity ofg s could not be documented due to large scatter ofg s (around 80 S m(-2)).c p behaved voltage sensitive with a notch of about 20 mF m(-2) around -180 mV, a peak of about 40 mF m(-2) at -120 mV and vanishing at -70 mV. When these data are compared with the predictions of nonsteady-state electrical properties of charge transport systems (U.-P. Hansen, J. Tittor, D. Gradmann, 1983,J. Membrane Biol. in press), model "A" (redistribution of states within the reaction cycle) consistently provides magnitude and voltage sensitivity of the elementsg o ,g s andc p of the equivalent circuit, when known kinetic parameters of the pump are used for the calculations. This analysis results in a density of pump elements in theAcetabularia plasmalemma of about 50 nmol m(-2). The dominating rate constants for the redistribution of the individual states of the pump in the electric field turn out to be in the range of 500 sec(-1), under normal conditions.